If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6} then prove the following :
A' = {5, 6, 7, 8, 9}

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Solution

$A = {1, 2, 3, 4}$
$U = {1, 2, 3, 4, 5, 6, 7, 8, 9}$
$A^{'} = U - A = {5, 6, 7, 8, 9}$
Hence proved.

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If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6} then prove the following :A' = {5, 6, 7, 8, 9}

A={1,2,3,4}U={1,2,3,4,5,6,7,8,9}A′=U−A={5,6,7,8,9}Hence proved.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4}, B = {2, 4, 6, 8}, C = {3, 4, 5, 6} then prove the following :
A' = {5, 6, 7, 8, 9}

$A = {1, 2, 3, 4}$
$U = {1, 2, 3, 4, 5, 6, 7, 8, 9}$
$A^{'} = U - A = {5, 6, 7, 8, 9}$
Hence proved.